Investigating representations of high-spin hadron wave function in the Regge framework

The vector-spinor $\psi^{\mu}=\psi \otimes e^{\mu}$ is the standard representation of Rarita-Schwinger field for particle of spin-3/2. In this work we search for the solution for spin-3/2 spinor legitimate to describe hadron reactions at high energy and show that the representation of $1 \otimes {1\over2}$ state composed of each helicity eigenstate should yield the same result as the one combined by the momentum states from boosting spin-1 and spin-1/2, respectively. Proofs are given in numerical consequences of differential cross section and spin density matrix elements in the $\gamma + N\to\pi +\Delta(1232)$ process. In the similar fashion, the two respresntations discussed above are applied for tensor field $e^{\mu\nu}=e^{\mu}\otimes e^{\nu}$ and numerical results in the process $\gamma+ N\to f_2(a_2) +N$ are presented for proof of equality.